Saturday, 7 January 2017

At some point over the Christmas break I was cursing the fact that I was finding it difficult to find a weather map. That is a weather map with isobars and fronts marked on it not one with icons of cloud, rain and sun. My favourite subject as a final year physics student was Atmospheric Physics: I was fascinated by how the differential equations delivered different weather, particularly cloud formations, based on different inputs. Underpinning this academic interest my father taught me to sail and until I left the oil industry for academia, and lost money and free time as a result, I was a keen sailor. This has left me with the ability to formulate my own idea of the future weather from pressure charts, and my expertise is such that my wife confidently ignores it. Though I find pressure charts more useful than the rain icons, which I believe replace the cloud icon with a rain icon when 26 out of the 50 simulations the MetOffice runs return rain.

Meteorology also featured in a discussion of "fog" and "mist", on the BBC Radio 4's Today programme. The meteorologist distinguished the two identical phenomenon in terms of visibility: fog is less than 1,000 m, mist indicates visibility is 1,000m-2,000m and they said terms like "thick fog" or "dense fog" are meaningless. I checked my 1998 RYA Weather forecast book, where it said shipping forecasts do distinguish fog (200m-1000m), thick fog (50m-200m) and dense fog (less than 50m). The distinctions the meteorologist was making come from aviation forecasts and they were ignoring maritime definitions, that describes visibility of 1,000m-2,000m as "Poor visibility", since it can be caused by mist, dust or smoke.

Two things struck me about these experiences. Firstly the meteorologists definition reflected the relative significance of modern aviation over shipping, the public forecast definitions reflected this change in status, definitions were mutable to social status. The weather map issue is more significant in that the maps it uses today provide the public with "the answer" (there is a 52% chance of rain tomorrow, here is a rain icon that is interpreted as rain) rather than the information to make a judgement. I see this is an example of the transformation of the public sphere, where by a state institution inhibits the public's ability to think and criticise. I think this type of transformation in relation to finance as being core to the lack of faith the public have in finance and the public's inability to knowledgeably criticise finance the root of financial crises.

A key episode in the transformation of finance was the 1844 Bank Charter Act. This was a consequence of twenty years debate amongst economists on the merits of fixing the relationship between money and gold. The currency school argued, with the support of statistics, that the easy availability of credit led to inflation and so there should be a link between the, concrete, quantity of gold and the availability of credit. The banking school argued that financial instability was a consequence of fluctuations in demand and supply and had nothing to do with the networks of banks providing credit by issuing their own notes. This argument was supported by the fact that high, not low, interest rates were associated with periods of inflation. The currency school won the argument and the Bank Charter Act prohibited English banks, other than the Bank of England, from issuing notes and required all banks to hold Bank of England notes as a capital reserve to back up their lending. Banks could still create ‘money’ in bank deposits by lending money, which would be ‘destroyed’ once the loan was repaid but were under the centralised control of the Bank of England.

In the aftermath of the Bank Charter Act the Quaker dominance of banking waned. The Act undermined the network of ‘country’ banks that served local businesses and led to the merger and centralisation of the provincial Quaker institutions. Following this centralisation a number of Quakers became associated with financial malfeasance. The most famous example is the failure of Overend, Gurney & Company in 1866. The firm was connected to the Quaker Gurney banking dynasty and had been able to underwrite other banks during a crisis of 1825. Its failure was a result of speculative investing in the 1850s, exposed by the Panic of 1866, and the refusal of the Bank of England to underwrite it. In the distributed financial network that existed before 1844 the stability of the system rested on inter-personal relationships and trust. Quaker doctrine nurtured this trust and produced financial success. After 1844 this stability rested on the centralised decision making of the ‘lender of last resort’.

On this basis I was interested to hear that Andy Haldane, Chief Economist at the Bank of England had also drawn connections between finance and weather forecasting in a speech hosted by the Institute of Government (the relevant section is initiated at 15:22 and then developed at 18:45 in this video)

Dr Haldane compares economists' failures to foresee the Credit Crisis with the the BBC's lunctime weather forecast of 15th October 1987

Note that the forecaster starts by dismissing the prospect of a hurricane hitting the UK raised by a member of the public. The following day the BBC reported a "hurricane" had struck the UK overnight causing the death of 18 people. It is ironic that the BoE looks back to the weather event of 15 October 1987, skilfully passing over Black Monday of 19 October 1987.

Dr Haldane observes that the accuracy of weather forecasts has improved dramatically since 1987 through the greater use of data and economics could similarly improve (19:53-20:10). I would start of by disputing Dr Haldane's diagnosis and argue it was not greater data (10 weather ships used in the 1970s have been replaced by 18 weather buoys) that lead to the improved forecasts but greater computational power that has allowed finer scale simulations of the differential equations that has delivered the better precision. Whether or not the improvement in forecast accuracy is down to greater data or greater computational power the underlying assumption is that the economy, like the weather, is a system that can be represented by a set of differential equations that can be used to simulate the evolution of the economy. This is a massive assumption.

Both Aristotle and Cicero recognised that it was feasible to predict natural phenomena, like the weather but events subject to human agency were impossible to foresee. Augustine agreed that humans were not able to foresee the future though the Christian God, unlike the pagan gods, had perfect fore-knowledge. The change in attitude begins with Descartes search for certainty that involved applying the deductive reasoning presented in Euclid's Elements to non-mathematical thinking starting from the ‘common notion’ “I think therefore I am”. This resulted in Descartes seeking mechanical, logical, explanations for natural phenomenon, rather than the teleological ones of Aristotle. Because different objects had different ends, Aristotle believed there were distinctive sciences to account for different phenomenon. Descartes, in contrast, believed in a unified science and he likened his whole philosophical programme to a tree whose roots were in metaphysics while its trunk was made up of mathematics ‒ “on account of the certitude and evidence of [its] reasoning” ‒ and physics with the branches of the tree being the practical sciences, both natural and moral. Both Dr Haldane's association of economics and meteorology, a consequence of a belief in unified science, and his search for certainty, revealed (19:41-19:48) by his admiration of precision in weather forecasts, reflect a commitment to Cartesian science.

The alternative to Descartes has traditionally been Locke who dismissed the Cartesian belief that there are innate ideas, rather people are born with minds that are blank-sheets: tabula rasa. Locke argued that knowledge came from experience with sense organs first perceiving events in the real world and then the mind interpreting them to form ideas. The validity of an idea did not depend on how it conformed to some authority, theoretical or political, but on the origins of idea and how had it evolved: its genealogy. This meant that people needed to investigate the origins of their beliefs, reflecting a Puritan upbringing. For Locke the purpose of philosophy was to show how the tabula rasa was filled with knowledge, which is “the perception of the agreement” of two ideas. In contrast to Descartes Locke argued that human knowledge could never be certain. One might observe the Sun rising every morning of our lives and infer it will do the same tomorrow, but we cannot assume it is true and this motivates us to ask ourselves why the Sun rises. Locke finished the An Essay concerning Human Understanding by dividing knowledge into three types. The first is physica, the nature of things. The second is practica, what people should do as rational and wilful agents. The final type is semeiotika (Greek for ‘signs’), how physica and practica are attained and communicated.

Locke applied these ideas to politics in his Two Treatises of Government. As a Puritan who had lived through the Civil War, Commonwealth and Restoration, Locke had been concerned with the fundamental tension between an individual’s right to sincerely express their religious beliefs and the need for a well ordered society to mandate the restriction of those rights, such as by a sovereign’s exercise of prerogative powers. Locke argued that a state was made up of autonomous individuals ruled by rationally constituted, abstract and universal laws rather than by subjects enforced to comply with the personal decrees of monarchs.

While Descartes philosophy can be caricatured as being based on doubt, Locke’s can be characterised as focusing on trust with Locke claiming that language was important because it enabled promises to be made , which created the trust that bound a society together. Since knowledge was fallible reliable knowledge could only be based on trust, faith is only necessary in the presence of doubt, while a stable political system relied on people making and keeping promises and abiding by contracts. Locke opposed atheism because it dissolved trust by undermining individuals’ commitment to truth telling, promise keeping and consideration for others.

Locke's influence was persistent. The tripartite separation of knowledge into physica, practica and semeiotika was mirrored in Kant's tripartite Critique of Pure Reason, Critique of Practical Reason and Critique of Judgement. Laplace’s reputation in mathematics was built on two parallel pairs of books: Mécanique Céleste (1799-1825) and Exposition du système du monde (1796) describing the mathematics of physica to a technical and general audience, while Théorie analytique des probabilités (1812) and Théorie des probabilités (1819) did the same for the mathematics of practica.

Descartes view of a certain, unified science came to dominate during the nineteenth century. Descartes' ideas had been developed by Spinoza who's Deus sive natura,
‘God or nature’, indicated that there was only a single substance that,
when viewed from one perspective is nature but from another is God.
This solved the problem of how Descartes’ mind interacted with matter at
the cost of prohibiting contingency, because if everything is connected
to God, it cannot happen randomly. Spinoza argued that people believe themselves to
possess free-will and have autonomy because, being only finite, they do not see the complete
picture. The purpose of human rationality was to
come to understand the true nature of God, the laws of nature. Spinoza
believed that at the most basic level people have direct knowledge of
nature through their senses. This can be improved into a scientific
knowledge of the world that could identify connections between phenomena
and so was able to make generalisations. The ultimate aim was to have
direct knowledge of the generalisations, not mediated by ‘finite’ ideas
or concepts and this ‘third type’ of knowledge delivered true freedom.
Spinoza saw the purpose of the individual as to lift themselves out of a
mundane perspective in order to comprehend the totality of creation. Spinoza's
objective, described in his Ethics, presented in the Euclidean style, was of attaining a 'God-like' perspective was picked up by the
German Romantics and resulted in the Idealists assuming a deterministic outlook across a unified science.

Dr Haldane refers to a "methodological mono-culture" in economics (16:29-16:31). I think that the mono-culture is not a specific to neo- or
new-Keynesianism or Marxism etc. etc. but to the fact that they are all based on the Cartesian tradition that results in 'rationality' coming to signify a
commitment to deterministic certainty.

I suspect Dr Haldane would regard these points as reading a little too much into what he has said in an informal setting, in much the same way a patient may dismiss a line their psychiatrist takes. However, I think the distinction between a Lockean and Cartesian approach to economic policy making is fundamental to the issues the BoE is facing up to. Consider the issue of market liquidity. For most of the period since 1700 liquidity, the ability to transact at will, had been associated with a person's credit, Defoe discussed it frequently. A person's credit was based on their trustworthiness and the financial system was founded on believing 'promises to pay'. Today much of the research on liquidity, some of it funded by the BoE, seems to see 'liquidity' as a utility that is the responsibility of the regulator. This tends to focus on defining the capital reserves of institutions, based on the assumption that the economy is a deterministic system, and ignores the Lockean issue of trust. I suspect these points have broader relevance in the whole issue around "post-truth" politics: people who think there is an issue seem to have lost the faith of the public.

Some post-scripts:

Proofs that the economy is not deterministic are fairly straight forward to construct. Locke and Spinoza would agree that peoples' beliefs are formed by their experiences and inform their decisions. Hence, whether or not a person has a conversation with another determines the future. The economy can only be predictable if individual interactions are predictable. This is only possible if all peoples deaths are predictable, which is not the case since earthquakes and hurricanes are not predictable. It might be admirable to aspire to identifying the equations that represent the economy and amass the data, but in the meantime I think it would be better to focus on what is important and achievable in an uncertain world, such as restoring public trust in economics.

It might seem odd that a mathematician is sceptical about the Euclidean method. Most mathematicians appreciate that a proof of a theorem starts at the result and the process of working out what is required to deliver the proof. This approach to organising science was the great contribution of the ancient Greeks and was rooted in Platonic Forms, which needed to be the foundations of knowledge. This fact about Euclid was not really appreciated until Frege in the 1880s and resulted in Descartes belief in innate ideas and justified Kant's synthetic a priori truths. Its a great way of 'proving' the conclusion you want to, with Hobbes being the first great exponent.

An interest. I submitted a grant application to the BoE in spring 2016 for funds to model, mathematically, the effect that trust might have on the resilience and effectiveness of financial networks. It was declined.

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.